Laustsen, Niels Jakob
(2012)
*A very proper Heisenberg-Lie Banach *-algebra.*
Positivity, 16 (1).
pp. 67-79.
ISSN 1385-1292

Official URL: https://doi.org/10.1007/s11117-011-0111-2

## Abstract

For each pair of non-zero real numbers q_1 and q_2, Laustsen and Silvestrov have constructed a unital Banach *-algebra C_{q_1,q_2} which contains a universal normalized solution to the *-algebraic (q_1,q_2)-deformed Heisenberg-Lie commutation relations. We show that in the case where (q_1,q_2) = (1,-1) or (q_1,q_2) = (-1,1), this Banach *-algebra is very proper; that is, if M is a natural number and a_1,..., a_M are elements of either C_{1,-1} or C_{-1,1} such that a_1^*a_1 + a_2^*a_2 + ... + a_M^*a_M = 0, then necessarily a_1 = a_2 = ... = a_M = 0.

Item Type:

Journal Article

Journal or Publication Title:

Positivity

Additional Information:

2010 Mathematics Subject Classification: primary 46K10; secondary 43A20.

Uncontrolled Keywords:

/dk/atira/pure/researchoutput/libraryofcongress/qa

Subjects:

Departments:

ID Code:

34845

Deposited By:

Deposited On:

13 Dec 2010 16:11

Refereed?:

Yes

Published?:

Published

Last Modified:

01 Jan 2022 09:32